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Journal of Siberian Federal University. Mathematics & Physics, 2013, Volume 6, Issue 2, Pages 247–261
(Mi jsfu311)
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This article is cited in 8 scientific papers (total in 8 papers)
On the spectral properties of a non-coercive mixed problem associated with $\overline\partial$-operator
Alexander N. Polkovnikov, Aleksander A. Shlapunov Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia
Abstract:
We consider a non-coercive Sturm–Liouville boundary value problem in a bounded domain $D$ of the complex space $\mathbb C^n$ for the perturbed Laplace operator. More precisely, the boundary conditions are of Robin type on $\partial D$ while the first order term of the boundary operator is the complex normal derivative. We prove that the problem is Fredholm one in proper spaces for which an Embedding Theorem is obtained; the theorem gives a correlation with the Sobolev–Slobodetskii spaces. Then, applying the method of weak perturbations of compact self-adjoint operators, we show the completeness of the root functions related to the boundary value problem in the Lebesgue space. For the ball, we present the corresponding eigenvectors as the product of the Bessel functions and the spherical harmonics.
Keywords:
Sturm–Liouville problem, non-coercive problems, the multidimensional Cauchy–Riemann operator, root functions.
Received: 10.01.2013 Received in revised form: 10.01.2013 Accepted: 20.01.2013
Citation:
Alexander N. Polkovnikov, Aleksander A. Shlapunov, “On the spectral properties of a non-coercive mixed problem associated with $\overline\partial$-operator”, J. Sib. Fed. Univ. Math. Phys., 6:2 (2013), 247–261
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https://www.mathnet.ru/eng/jsfu311 https://www.mathnet.ru/eng/jsfu/v6/i2/p247
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Abstract page: | 334 | Full-text PDF : | 76 | References: | 35 |
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